Disordered magnetic lattice gas: Formulation by the method of the distribution function

Abstract

A spin-1 model of a disordered magnetic lattice gas with magnetic and nonmagnetic interactions is presented as an extension of the magnetic gas introduced in the previous paper. A formulation using the method of the distribution functions is given. The concept of an effective potential is introduced along with the usual effective field in order to describe this system. Integral equations for the distribution functions are derived as a natural extension of the Bethe-Peierls-Weiss approximation to the disordered magnetic system. The form of the thermo-dynamic potential is given and shown to be stationary for the distribution function which satisfies the integral equation. The relationship of t..